...and, just as there [at the games] it was a very high-minded thing to look on [as one] acquiring nothing for oneself, so in life the contemplation of things and their investigation stood far above all pursuits.

Thanks, I suppose this functions as in Greek, then. By the way, I never quite figured out how angular parentheses <> are to be used, as opposed to square ones [] and rounds. Perhaps there are varying practices. How appropriate is my above use, for instance? I've tried to look it up, but never found a satisfactory answer. (In an English selection from Aristotle (Irwin) they are used for gloss, but I suspect this is unconventional.)

In the convention I follow, a ( parenthesis bracket indicates an aside in the speaker's voice, a [ square bracket indicates an aside in a commentator's voice on another's voice or indicates something that could be dropped, and an angle < bracket introduces a hidden voice (in a computer language, say).

I know the mathematical use from the bac, but it never occured to me that exclusive interval delimiters had anything to do with greater than signs. As I remember it, [3--5] is an inclusive interval, such that, if we are dealing with integers, it = {3,4,5}; whereagainst [3--5> is exclusive at the end and = {3,4}. I'm not convinced that that has anything to do with inequality. Further, if you think the text critical use is derived from the mathematical, that's far from obvious, and requires some argument or source as well.

Lavrentivs wrote:...but it never occured to me that exclusive interval delimiters had anything to do with greater than signs...I'm not convinced that that has anything to do with inequality. Further, if you think the text critical use is derived from the mathematical, that's far from obvious, and requires some argument or source as well.

Since I said none of those things and think none of those things, don't be bothered by any of those silly things, though [3--5> may be considered as meaning from 3 to less than 5 (a number 5 is greater than), if you want to think that way. However, I know open intervals as ]3,5[ or (3,5) for 3 < x < 5, or [3,5[ or [3,5) for what you wrote above (3 <= x < 5). If you use <3--5> for 3 < x < 5, fine, though I don't recognize that, or if you use >3--5>, fine, too, for 3 < x < 5, though I don't recognize that. I do recognize "--" (two hyphens) as a replacement for an n-dash meaning "to" in typescripts before the days of computers and more accurate representations of an n-dash, and also their being used as an m-dash, but not everyone cares about hyphens, n-dashes and m-dashes.

This is a square bracket: [ &#91;, Unicode character Left Square Bracket U+005B
This is a curly bracket: { &#123;, Unicode character Left Curly Bracket U+007B
This is a round bracket: ( &#40;, Unicode character Left Parenthesis U+0028
This is a chevron or broken or angle bracket: ⟨ (&#12296;), Unicode character Left Angle Bracket U+3008
This is a chevron or broken or angle bracket: ⟨ &#9001;, Unicode character Left-pointing Angle Bracket U+2329
This is a corner bracket: ｢ &#12300;, Unicode Left Corner Bracket U+300C.
This is an angle quotation mark: &#8249; Unicode character Left-pointing Angle Bracket U+2329
This is a mathematical white-square bracket, &#10214;, Unicode character Mathematical Left White Square Bracket U+27E6.
This is a mathematical white curly bracket, &#10627;, Unicode character Mathematical Left White Curly Bracket U+2983.
This is a black tortoise shell bracket, &#10647;, Unicode character Left Black Tortoise Shell Bracket U+2997.
This is a mathematical white tortoise shell bracket, &#10220;, Unicode character Mathematical White Tortoise Shell bracket U+27EC.
This is a mathematical angle bracket, ⟨ &#10216;, Unicode character Mathematical Left Angle Bracket U+27E8. Note its height.

This, however, is an inequality sign: < <, Unicode character Less-than sign, U+003C. It is not as tall as the mathematical angle bracket.

Modernly, especially in coding, many use the Unicode inequality sign as an angle bracket because it's in front of their nose on the keyboard. As I said, you are using an inequality sign for an angle bracket, because the sign that is in plain sight on your keyboard is officially called an inequality sign and it's of lesser height than the mathematical angle bracket. It is a common practice to use that key character as an angle bracket. It is not an offence. You don't break any law.

On the other hand, I don't know that unicode is a typographical authoritiy; such are to my mind (some of) the books that were printed before typography ceased to be a craft. Looking, f. ex., at Burnet's edition of Ethica Nicomachea printed in London 1900, the chevrons are not tall. Gauther's and Jolif's Èthique à Nicomaque, Paris, 1958, have taller chevrons, but also much broader than the ones in unicode. I doubt that either of these should have employed a different sign were it in need of signifying an inequality. Finally, neither Adobe Caslon Pro nor Garamond Premier Pro has chevrons distinct from inequalities. (And yes, I know my apostrophes aren't apostrophes, and normally I care, but I'm on a Windows computer that isn't mine and I can't be bothered finding out how to produce proper ones. Besides, this sans serif arguably isn't worth it.)

The Unicode standard certainly is an authoritative standard and has been drawn up by many typographical authories. I'm sure you will find many variations over time. Maybe your computer can't display them or the applications you use can't display then, because otherwise you would see that both Adobe Caslon Pro and Garamond Premier Pro do exhibit the differences I was talking about between inequality signs and chevrons or angle brackets in the Unicode standard.

Really? Perhaps you are thinking of the difference between single guillemets and inequalities. Given this choice, I think one should use inequalities and not guillemets for chevrons. Or are you seeing something that I am not? Do you use XeLaTeX? If so, which commands would you use to produce your different characters?

By this principle taken as universal, one should ideally use a symbol for the apostrophe which were different from that for the closing single quotation mark. I admit that in this case it seems more logical to have a symbol that is more like ( [ {, but so long as this isn't found in a book that is older than digital printing, I'll allow myself to consider it less than obligatory.

The reason why it isn't found is perhaps that its use was very limited (to philology). To my mind, taking what one has is such a case, has a certain charm to it. (It resembles the case of the first universal quantifiers in Frege, which are just inverted As, hanging below the line. Here, using an actual A instead of some sans serif special symbol adjusted above the line is preferable.)

Sorry, Laurentius. This is a forum for learning latin. Elsewhere you might learn about displaying Unicode characters and about chevrons in pre-digital books. Showing you where to look for chevrons won't help my or your latin.

You asked for help with understanding brackets, not me. Some people have other agendas. Possibly, they want to try to show off. I admit the defeat of apparently not getting through. I regret that, but why should I respond with conviction to willful non sequiturs and deaf ears. At a certain point, one has to concede that all effort spent has been a waste of time. I'll happily respond away to questions about latin, if I can. Possibly, you're just having a laugh.

If you have forgotten, just raise your eyes.Si oblivisceris, modò tolle oculos.

Lavrentivs wrote:By the way, I never quite figured out how angular parentheses <> are to be used, as opposed to square ones [] and rounds. Perhaps there are varying practices. How appropriate is my above use, for instance? I've tried to look it up, but never found a satisfactory answer. (In an English selection from Aristotle (Irwin) they are used for gloss, but I suspect this is unconventional.)

adrianus wrote:There are, indeed. Strictly, "<>" aren't really angular brackets, or chevrons, at all. They are inequality signs, but it's no big deal, and they're used as brackets in lots of places, including for coding.

"You did, not me" is everyday, informal parlance in English and in formal parlance, too. "You did, not me" is by far the more usual form in English, much more so than "You did, not I." (See Cambridge Grammar of the English Language, p.461, §16.2.1[14]). You say I should not write that. Utter nonsense. And you say I'm a pedant? Repeat, please: "It is not me who is a pedant. It is I who am a pedant."

Lavrentivs wrote:By this principle taken as universal, one should ideally use a symbol for the apostrophe which were different from that for the closing single quotation mark.

When the symbols differ, professional typesetters prefer to use the proper symbols. A professional publishing company would not print something with ' for an apostrophe, or " for a quotation mark - they would use ’ and “ or ” respectively. The closing single quotation mark is identical in form and Unicode character to the apostrophe.

All human rules have exceptions, but this is indeed the rule and not the exception for professional writing. For unprofessional composition, such as posts on a web forum, it is far too much hassle for most, myself included, to use these symbols.

What do you mean, exactly? Apostrophes and closing single quotes are identical in form and digital real estate, whereas chevrons and greater than symbols are not. If there were two torrent Unicode designations for the apostrophe and single double quote, they would probably be used accordingly as a matter of principle, as there are always benefits in including as much data as possible, but at a visual level there would be no difference. I can tell a greater than symbol from a chevron, but context alone distinguishes between apostrophes and closing quotes.

Adrian said, arguing that chevrons should be visually different from inequalities, that a good typesetter would always choose different symbols for expressing different meanings. My point was simply that eodem ratione apostrophes indistinguishable from quotation marks would be unacceptable, and that we must therefore reject this principle. If apostrophes can be represented by the same symbol as quoatation marks, chevrons can be represented by the same symbol as inequalities. (As they are in traditional typography.)

Closing quotes have always been inverted commas as have apostrophes, but chevrons are not and never have been inequality symbols. They are represented by them in computing for convenience, but not, as you say, in traditional typography. What you are arguing is if these two glyphs are unique, then all glyphs should be unique. Non sequitur.

On a professionally printed page, apostrophes and closing quotes should be identical, and chevrons and inequality symbols should be different. There is nothing philosophically wrong with designating separate but identical symbols to apostrophes and quotes, but there is nothing typographically wrong with continuing to use one for both. There is, however, a visible difference between chevrons and inequality symbols, which does not enter into the apostrophe and quote comparison, that is professionally unacceptable when one or the other is required. It is this visible aspect, not the philosophical aspect that Adrian and I are referring to.

As has been said, this doesn't matter so much for everyday computing, since we have easy access only to inequality symbols. But, by your line of reasoning, chevrons should be altogether merged with inequality symbols, and く (in the Japanese syllabary) may as well be merged with < because they look similar.

I challenge you to put your question in a more appropriate forum, where you can also challenge people to demonstrate Unicode characters in particular fonts.Te invito ut in alio foro aptiore roges, quo tu alios invites ut characteres Unicode quorumdam scripturae demonstrent.

I can't perform delicate search operations from my phone, but I can refer you to Wikipedia. Find angle brackets in the usage section, where it discusses the mathematical and linguistic uses of the punctuation, and specifically addresses the issue of replacing them with inequality symbols.